Given an algebraic differential equation of order greater than one, it is shown that if there is
any nontrivial algebraic relation amongst any number of distinct nonalgebraic solutions …

Several results on the birational geometry of algebraic vector fields in characteristic zero are
obtained. In particular,(1) it is shown that if some cartesian power of an algebraic vector field …

We prove an analogue of the Lindemann-Weierstrass theorem (that the exponentials of a
$\mathbb {Q} $-linearly independent set of algebraic numbers are algebraically …

A differential-algebraic geometric analogue of the Dixmier–Moeglin equivalence is
articulated, and proven to hold for D-groups over the constants. The model theory of …

Let S be a semiabelian variety over an algebraically closed field, and let X be an irreducible
subvariety not contained in a translate of a proper algebraic subgroup of S. We show that the …

We give accounts and proofs, using model-theoretic methods among other things, of the
following results: Suppose∂ y= Ay is a linear differential equation over a differential field K …

We provide a characterisation of differentially large fields in arbitrary characteristic and a
single derivation in the spirit of Blum axioms for differentially closed fields. In the case of …

We prove that the Poisson version of the Dixmier–Moeglin equivalence holds for
cocommutative affine Poisson–Hopf algebras. This is a first step towards understanding the …

Non-n-ampleness as denned by Pillay [20] and Evans [5] is preserved under analysability.
Generalizing this to a more general notion of Σ-ampleness, this gives an immediate proof for …

The ample hierarchy of geometries of stables theories is strict. We generalise the
construction of the free pseudospace to higher dimensions and show that the n-dimensional …